Question

A publisher reports that 48% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually under the reported percentage. A random sample of 100 found that 43% of the readers owned a particular make of car. Is there sufficient evidence at the 0.10 level to support the executive's claim?

Step 1 of 7: State the null and alternative hypotheses.

Step 2 of 7:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7:

Specify if the test is one-tailed or two-tailed.

Step 4 of 7:

Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7:

Identify the value of the level of significance.

Step 6 of 7:

Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7:

State the conclusion of the hypothesis test.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.48
Alternative Hypothesis, Ha: p < 0.48

2)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.43 - 0.48)/sqrt(0.48*(1-0.48)/100)
z = -1.00

3)

One tailed test

4)

P-value Approach
P-value = 0.1587

5)

0.10 is level of significance

6)

As P-value >= 0.1, fail to reject null hypothesis.

7)

There is not sufficient evidence to conclude that the percentage is actually under the reported percentage